Monte Carlo and Multilevel Monte Carlo Methods with Applications in Financial Engineering

Abstract

We undertake an in-depth investigation of the Monte Carlo simulation approach and its various extensions to tackle computationally demanding problems that frequently arise in the field of Quantitative Finance. Specifically, we concentrate on three major domains: derivative pricing, risk management, and portfolio optimization, each of which involves significant computational complexity. By leveraging advanced Monte Carlo techniques, we aim to improve numerical efficiency, accuracy, and convergence rates in these financial applications.